This invention is in the field of communications, and is more specifically directed to multicarrier modulation communications, such as Digital Subscriber Line (DSL) communications.
An important and now popular modulation standard for DSL communication is Discrete Multitone (DMT). According to DMT technology, the available spectrum is subdivided into many subchannels (e.g., 256 subchannels of 4.3125 kHz). Each subchannel is centered about a carrier frequency that is phase and amplitude modulated, typically by Quadrature Amplitude Modulation (QAM), in which each symbol value is represented by a point in the complex plane. The number of available symbol values for each subchannel, and thus the number of bits in each symbol communicated over that subchannel, is determined during initialization of the DMT communications session. The number of bits per symbol for each subchannel (i.e., the “bit loading”) is determined according to the signal-to-noise ratio (SNR) at the subchannel frequency, which is affected by the transmission channel noise and the signal attenuation at that frequency. For example, relatively noise-free and low attenuation subchannels may communicate data in ten-bit to fifteen-bit symbols, represented by a relatively dense QAM constellation with short distances between points in the constellation. On the other hand, noisy channels may be limited to only two or three bits per symbol, allowing a greater distance between adjacent points in the QAM constellation. Typically, the SNR of some subchannels is so poor that these subchannels are unloaded, carrying no bits. DMT modulation thus maximizes the data rate over each subchannel, permitting high speed access to be carried out even over relatively noisy and attenuated twisted-pair lines.
DMT modulation also permits much of the signal processing to be carried out in the digital domain. Typically, a serial digital datastream to be transmitted incoming bitstream is arranged into symbols, one for each subchannel, with the symbol size depending on the bit loading as noted above. Reed-Solomon coding and other coding techniques are typically applied for error detection and correction. Modulation of the subchannel carriers is obtained by application of an inverse Discrete Fourier Transform (IDFT) to the encoded symbols, producing a discrete modulated time domain signal having signal components that are associated with each of the sub-carrier frequencies. This modulated signal is then serially transmitted. All of these DMT modulation operations can be carried out in the digital domain, permitting implementation of much of a DSL modem, and particularly much of the processing-intensive operations, in a single chip such as a Digital Signal Processor (DSP).
The discrete output time domain signal from the modulation is converted into a time-domain analog signal by a conventional digital-to-analog converter, and is communicated over the transmission channel to the receiving modem, which reverses the process to recover the transmitted data. Ideally, the DMT subchannels in the received signal are orthogonal so that the signal can be demodulated by a Discrete Fourier Transform (DFT).
However, the non-ideal impulse response of the transmission channel of course distorts the transmitted signal. The signal received by the receiving modem can be considered to be a convolution of the transmitted analog signal with the impulse response of the transmission channel. One may express the time-domain signal y(n) at the receiver, based on a transmitted time-domain signal x(n), as:y(n)=x(n)h(n)
This expression simply states that the received signal y(n) is the time-domain convolution of the input signal x(n) with the channel impulse response h(n). In the ideal case, this time-domain expression can be expressed in the frequency-domain as:Y(n)=X(n)·H(n)where X(n), H(n), and Y(n) are the respective frequency-domain representations of time-domain signals x(n), h(n), y(n). Considering that the transmitted signal x(n) is the IDFT of the symbol sequences at their respective subchannel frequencies, the frequency-domain spectrum X(n) corresponds to the symbols themselves. According to the DMT modulation technology, the receiver can therefore retrieve the symbols X(n) by removing the channel response H(n) from the DFT of the frequency-domain received signal Y(n). Preferably, this is performed by a single-tap frequency domain equalizer.
However, time domain convolution corresponds to frequency domain multiplication only if the input sequence is infinitely long, or if the input sequence is periodic. Because the number of subchannels is finite, however, the number of real-valued time-domain samples at the output of the transmitter IDFT (i.e., the “block” length) is also finite. Accordingly, it is useful to make the transmitted signal appear to be periodic, at a period on the order of the block length. A well-known technique for accomplishing this is to include a cyclic prefix with each transmitted block in the datastream. The cyclic prefix is generally defined as a number P of samples at the end of a block of samples in the output bitstream. These P samples are prepended to the block, prior to digital-to-analog conversion, so that the transmitted signal appears periodic. This apparent periodicity in the input sequence permits the use of a DFT to recover the modulating symbols in each subchannel, so long as the impulse response of the transmission channel, commonly referred to as the channel length, is less than the length of the cyclic prefix.
In effect, the cyclic prefix eliminates inter-symbol interference (ISI) between adjacent data frames, and inter-carrier interference (ICI) between subchannels. ISI generally arises from distortion and spreading of the transmitted signal over the channel, causing the end of one DMT symbol to overlap into the beginning of the next DMT symbol. ICI affects the independence of the subcarriers, resulting in loss of orthogonality among the subchannels, which in turn prevents separation of the modulating data on these subchannels at the receiver.
In order for the input sequence to appear periodic, so that the ISI interference is contained within the redundant prefix of the block, the cyclic prefix must be longer than the channel length. However, the effective data rate of the transmission is reduced by an amount corresponding to the length of the cyclic prefix. In the case of a signal with a block length of N samples and a cyclic prefix of P samples that is generated by prepending a copy of the last P samples of the block, the data rate is reduced by a factor:
  N      N    +    P  A tradeoff between interference and data rate is thus present in conventional DMT communications.
By way of further background, the peak-to-average ratio (PAR) of signal amplitudes in DMT transmissions is defined as the ratio of the peak power level, for a sample, to the average power level over a sequence of samples in DMT transmissions without involving a loss of data rate. A method of reducing the PAR is described in Gatherer and Polley, “Controlling clipping probability in DMT transmission”, Proceedings of the Asilomar Conference on Signals, Systems, and Computers, (1997), pp. 578–584, incorporated herein by this reference. According to this approach, the PAR is reduced by using unloaded subchannels, which are unsuitable for carrying data because of noise or attenuation, to carry a “signal” that contains no payload. This signal on the unloaded subchannels is selected to have the effect of reducing the amplitude of the time domain signal to below the PAR amplitude threshold, in most cases.